SSC CGL 2023 Tier-I Official Paper (Held On: 18 Jul 2023 Shift 1) (Previous Year Paper)

Given statement : 10 - 4 + 13 ÷ 15 × 3 = 71 

According to the question, after interchanging the signs :

So,

• Option - (1) : + and ×

10 - 4 + 13 ÷ 15 × 3 = 71 ⇒ 10 - 4 × 13 ÷ 15 + 3 = 71

10 - 4 × 0.87 + 3 = 71 

10 + 3 - 3.48 = 71

13 - 3.48 = 71

9.52 ≠ 71 (LHS ≠ RHS)

• Option - (2) : - and ÷

10 - 4 + 13 ÷ 15 × 3 = 71 ⇒ 10 ÷ 4 + 13 - 15 × 3 = 71

2.5 + 13 - 15 × 3 = 71

2.5 + 13 - 45 = 71

15.5 - 45 = 71

29.5 ≠ 71 (LHS ≠ RHS)

• Option - (3) : ÷ and ×

10 - 4 + 13 ÷ 15 × 3 = 71 ⇒ 10 - 4 + 13 × 15 ÷ 3 = 71

10 - 4 + 13 × 5 = 71

10 + 65 - 4 = 71

75 - 4 = 71

71 = 71 (LHS = RHS)

• Option - (4) : - and ×

10 - 4 + 13 ÷ 15 × 3 = 71 ⇒ 10 × 4 + 13 ÷ 15 - 3 = 71

10 × 4 + 0.87 - 3 = 71 

40 + 0.87 - 3 = 71

40.87 - 3 = 71

37.87 ≠ 71 (LHS ≠ RHS)

Hence, "Option - (3)" is the correct answer.

Given : BRU_TLP_RUI_LPBR_ITLPB_UIT_ _    

By checking options :

1. IBTRUPL → BRUITLPBRUITLPBRUITLPBRUITLP → (It doesn't Follows the pattern)
2. IBTUPLR → BRUITLPBRUITLPBRUITLPBRUITLP → (It doesn't Follows the pattern)
3. IBRUTLP → BRUITLPBRUITLPBRUITLPBRUITLP → (It doesn't Follows the pattern)
4. IBTURLP → BRUITLPBRUITLPBRUITLPBRUITLP → (It follows the pattern of : BRUITLP - BRUITLP - BRUITLP - BRUITLP)

⇒Option - (4) gives the pattern of "BRUITLP - BRUITLP - BRUITLP - BRUITLP"

Hence, "IBTURLP" is the correct answer.

According to given figure:

The figure will appear when it is opened as follows:

Hence, "Option - (3)" is the correct answer.

The figure that will replace the question mark (?) in the following figure series is shown below:

1. For line element → Number of lines within the given pentagon are increasing subsequently.

 

Final series is :

Hence, ‘option - (1)’ is the correct answer.

Logic :

1. (1^st number × 2) = 2^nd number
2. 3^rd number - 2^nd number = 22

Given :

• (16, 32, 54)

16 × 2 = 32

32 = 32 (LHS = RHS)

And,

54 - 32 = 22

22 = 22 (LHS = RHS)

• (29, 58, 80)

16 × 2 = 32

32 = 32 (LHS = RHS)

And,

54 - 32 = 22

22 = 22 (LHS = RHS)

So,

• Option - (1) : (17, 35, 59)

17 × 2 = 35

34 ≠ 34 (LHS ≠ RHS)

And,

59 - 35 = 22

24 ≠ 22 (LHS ≠ RHS)

• Option - (2) : (25, 50, 62)

25 × 2 = 50

50 = 50 (LHS = RHS)

And,

62 - 50 = 22

12 ≠ 22 (LHS ≠ RHS)

• Option - (3) : (24, 48, 70)

24 × 2 = 48

48 = 48 (LHS = RHS)

And,

70 - 48 = 22

22 = 22 (LHS = RHS)

• Option - (4) : (23, 46, 62)

23 × 2 = 46

46 = 46 (LHS = RHS)

And,

62 - 46 = 22

16 ≠ 22 (LHS ≠ RHS)

Hence, "Option - (3)" is the correct answer.

The correct mirror image of the given figure when mirror is placed at MN is as shown below:

Hence, the correct answer is "Option - (4)".

Logic : Increasing odd number series is subtracted from each number subsequently.

So,

108 - 9 = 99

99 - 11 = 88

88 - 13 = 75

75 - 15 = 60

60 - 17 = 43

Hence, "75" is the correct answer.

The logic followed here is :- Common difference between the position value according to English alphabetic series is (4).

​So,

• Option - (1) : PTXB

​

• Option - (2) : MQUY

​

• Option - (3) : GKOS

​

• Option - (4) : HKNQ

​

Thus, out of all the options 'HKNQ' is the odd one out as the common difference between the position value according to English alphabetic series is (4).

​Hence, "HKNQ" is the correct answer.

Logic : (1^st number + 10) = (3^rd number - 2^nd number)

Given : 

• (9, 6, 25)

9 + 10 = 25 - 6

19 = 19 (LHS = RHS)

• (14, 5, 29)

14 + 10 = 29 - 5

24 = 24 (LHS = RHS)

So,

• Option - (1) : (27, 8, 29)

27 + 10 = 29 - 8

37 ≠ 21 (LHS ≠ RHS)

• Option - (2) : (18, 4, 42)

18 + 10 = 42 - 4

28 ≠ 38 (LHS ≠ RHS) 

• Option - (3) : (13, 9, 32)

13 + 10 = 32 - 9

23 = 23 (LHS = RHS)

• Option - (4) : (12, 8, 20)

12 + 10 = 20 - 8

22 ≠ 12 (LHS ≠ RHS) 

Hence, "Option - (3)" is the correct answer.

The least possible Venn diagram for the given statement is:

Conclusions:

I. Some ornaments are jewellery → Follow (As, all jewellery are gold and all gold are ornaments. So, as whole jewellery comes in gold which whole comes in ornaments therefore it is definitely true.)

II. Some metals are jewellery → Does not Follow (As, all metals are gold and all jewellery are gold. So, it is possible but not definitely true)

III. All jewellery are ornaments → Follow (As, all jewellery are gold and all gold are ornaments. So, as whole jewellery comes in gold which whole comes in ornaments therefore it is definitely true.)

So, Only conclusions I and Ill follow.

Hence, the correct answer is "Only conclusions I and Ill follow".

Given Statement : Looking at the picture on the wall, he said “My sister-in-law S’s husband Q's son N had a sister R”.

Thus, according to the final family tree S is the mother of R.

Hence, "Mother" is the correct answer.

Given:

 

• The image must not to be rotated

  

Hence, the correct answer is "Option - (3)".

Logic : (1^st number - 2^nd number) × 2 = (3^rd number - 5)

Given :

• (36, 21, 35)

(36 - 21) × 2 = 35 - 5

15 × 2 = 30

30 = 30 (LHS = RHS)

• (43, 19, 53)

(43 - 19) × 2 = 53 - 5

24 × 2 = 48

48 = 48 (LHS = RHS)

So,

• Option - (1) : (51, 34, 39)

(51 - 34) × 2 = 39 - 5

17 × 2 = 34

34 = 34 (LHS = RHS)

• Option - (2) : (48, 37, 25)

(48 - 37) × 2 = 25 - 5

11 × 2 = 20

22 ≠ 20 (LHS ≠ RHS)

• Option - (3) : (44, 20, 54)

(44 - 20) × 2 = 54 - 5

24 × 2 = 49

48 ≠ 49 (LHS ≠ RHS)

• Option - (4) : (35, 22, 34)

(35 - 22) × 2 = 34 - 5

13 × 2 = 29

26 ≠ 29 (LHS ≠ RHS)

Hence, "Option - (1)" is the correct answer.

Given statement : 

According to the question, after replacing the * signs :

So,

• Option - (1) : ÷, ×, -, =, ×

28 * 4 * 3 * 9 * 42 * 12 ⇒ 28 ÷ 4 × 3 - 9 = 42 × 12 

7 × 3 - 9 =  504

21 - 9 = 504

12 ≠ 504 (LHS ≠ RHS)

• Option - (2) : ÷, ×, =, +, +

28 * 4 * 3 * 9 * 42 * 12 ⇒ 28 ÷ 4 × 3 = 9 + 42 + 12

7 × 3 = 63

21 ≠ 63 (LHS ≠ RHS)

• Option - (3) : ÷, ×, +, =, -

28 * 4 * 3 * 9 * 42 * 12 ⇒ 28 ÷ 4 × 3 + 9 = 42 - 12

7 × 3 + 9 = 30

21 + 9 = 30

30 = 30 (LHS = RHS)

• Option - (4) : +, =, ÷, ×, +

28 * 4 * 3 * 9 * 42 * 12 ⇒ 28 + 4 = 3 ÷ 9 × 42 + 12

32 = 0.33 × 42 + 12

32 = 13.86 + 12

32 ≠ 25.86 (LHS ≠ RHS)

Hence, "Option - (3)" is the correct answer.

The figure that will replace the question mark (?) in the following figure series is shown below:

1. For '

' element → Shifting in the zig-zag pattern of : left above corner - center - left below corner - right below corner - left above corner.

• Shifting clockwise and anti-clockwise alternately.
• Rotation of 90º clockwise and anti-clockwise alternately.

2. For '

' element → Shifting in the zig-zag pattern of : left below corner - right below corner - left above corner - center - left below corner.

3. For '

' element →

4. For '

' element →

Final series is

Hence, ‘option - (2)’ is the correct answer.

Logic: Second no. = [(First no.)² + (First no.)]

Checking all the options:

1. (15, 240)

⇒ [(15)² + 15]

⇒ (225 + 15) = 240

2. (13, 180)

⇒ [(13)2 + 13]

⇒ (169 + 13) = 182 ≠ 180

3. (11, 132)

⇒ [(11)2 + 11]

⇒ (121 + 11) = 132

4. (16, 272)

⇒ [(16)2 + 16]

⇒ (256 + 16) = 272

Here, in (13, 180) different logic is followed from the others.

Hence, the correct answer is "Option (2)".

Given:

(5, 32, 7)

(4, 30, 14)

Logic: Second no. = [(First no.)² + Third no.]

(5, 32, 7) 

⇒ [(5)² + 7]

⇒ (25 + 7) = 32

(4, 30, 14) 

⇒ [(4)2 + 14]

⇒ (16 + 14) = 30

Checking all the given options:

1. (7, 60, 11) 

⇒ [(7)2 + 11]

⇒ (49 + 11) = 60

2. (6, 65, 13) 

⇒ [(6)2 + 13]

⇒ (36 + 13) = 49 ≠ 65

3. (7, 50, 21) 

⇒ [(7)2 + 21]

⇒ (49 + 21) = 70 ≠ 50

4. (8, 60, 9) 

⇒ [(8)2 + 9]

⇒ (64 + 9) = 73 ≠ 60

Here, (7, 60, 11) shows a similar relation to the given set of numbers.

Hence, the correct answer is "Option (1)".

Here, we use the table given below:

Given:

CXW, EVU, GTS, IRQ,?

Logic: (2) is added to the first letter's positional value and (2) is subtracted from the second and third letter's positional value.

Here, 'KPO' is the next term.

Hence, the correct answer is "Option (4)".

Given: 'CAPSULE'

Logic: Each vowel is changed to the previous letter in the English alphabet series and each consonant is changed to the following letter in the English alphabetical series.

After changing as per the logic:

CAPSULE → DZQTTMD

The third letter from the left end is Q and the third from the right end is T.

The letters R and S come between Q and T in the English alphabet series.

Here, the 'Two' alphabet comes between Q and T.

Hence, the correct answer is "Two".

Given:

Dog : Labrador → Labrador is a breed of dog.

Similarly,

Vegetable : Capsicum → Capsicum is a vegetable.

Here, 'Vegetable : Capsicum' is the correct pair.

Hence, the correct answer is "Option (1)".

Given: 'Dubai, Asia, Africa '

1. Dubai → City in Asia continent.
2. Asia → continent.
3. Africa → continent.

The Venn diagram is:

Hence, the correct answer is "Option (4)".

Here, we use the table given below:

The logic followed in the given pair:

BEAUTY : ZVXEJH →

FRAGILE : FNLKFXM →

Similarly, for 'BEYOND : ?' →

Here, 'BEYOND : EPRCJH' is the correct pair.

Hence, the correct answer is "Option (4)".

Here, we use the table given below:

Logic: Code is formed when (3) is added to the positional value of the given letters.

‘CBVQ’ is written as ‘652520’ →

‘FRJT’ is written as ‘9211323’ →

Similarly, 'EHLP' will be coded as:

Here, 'EHLP' is coded as '8111519'.

Hence, the correct answer is "Option (4)".

Here, we use the table given below:

The logic followed in the given code language:

‘FRISK’ Is written as ‘THLIQ’ →

'MOADS’ Is written as ‘QODQB’ →

Similarly, ‘WAGER’ will be written as:

 

Here, 'WAGER' is written as 'CYJPC'.

Hence, the correct answer is "Option (3)".

Here, we unfold the paper step by step:

Step 1:

Step 2:

Hence, the correct answer is "Option (1)".

The correct answer is 1928 Amsterdam.

Key Points

• The Indian men's hockey team clinched their first Olympic gold medal in the 1928 Amsterdam Olympics.
• This marked the beginning of India's long dominance in the field of hockey. It was a highly symbolic achievement spotlighting India's potential in international sports.
• The team did not concede a single goal across five matches, and they scored a total of 29 goals, establishing their supremacy in the tournament.
• Notably, Major Dhyan Chand, one of India's most legendary hockey players, played a pivotal role and scored a hat-trick in the finals against the Netherlands.
• This historic win initiated India's golden era in hockey, with the Indian team securing six consecutive golds in the Olympics from 1928 to 1956.
• The Indian hockey men’s team has won eight Olympic gold medals in all, six of them in a row (from 1928-1956) and added two more at Tokyo 1964 and Moscow 1980.

The correct answer is Deccan trap.

Key Points

• The Deccan trap, located in the central and western parts of India, is a major region where black soil is found.
• This soil is typically black due to the high concentration of metallic compounds and minerals, particularly iron compounds, that it contains.
• Black soil, also known as 'Regur' or 'Cotton Soil', is ideal for growing cotton and is hence named so.
• The soil has a high capacity to hold moisture and is very fertile, making it suitable for agriculture, particularly for the production of cash crops like cotton, sugarcane, and soybeans.
• Besides the Deccan trap, black soil can also be found in Gujarat, Madhya Pradesh, parts of Tamil Nadu, Andhra Pradesh, and Rajasthan.

Additional Information 

• Alluvial Soil:
• Alluvial soil is the most widely spread and important soil in India, covering about 40% of the land area.
• It is highly fertile and rich in potash, phosphoric acid, and lime which are ideal for the growth of sugarcane, paddy, wheat, and other cereal and pulse crops.
• These soils are extensively found in Northern plains and river valleys.
• They are derived from the depositional work of rivers and are replenished every year by floods.
• Red Soil:
• Red soil covers about 24% of the total geographical area of the country.
• These soils are mainly found in the low rainfall regions of Rajasthan, Punjab, Haryana, Madhya Pradesh, Maharashtra, Telangana, Andhra Pradesh and some parts of Tamil Nadu.
• They are rich in iron and potash but have less phosphoric content.
• Horticultural crops like oranges, figs, olives, and grapes are grown on a large scale in areas with red soils.
• Black Soil, or Regur Soil:
• Black soils cover about 15% of India, mainly in the Deccan Plateau.
• They are rich in calcium carbonate, magnesium, potash, lime, and are ideally suited for growing cotton.
• Also known as "Cotton Soil" due to its ability to retain moisture, it's prevalent in the states of Maharashtra, Madhya Pradesh, Gujarat, Andhra Pradesh, and Tamil Nadu.
• Laterite Soil:
• They are found in high rainfall and temperature areas of the Western Ghats, Eastern Ghats, Northeast states, and the Andaman and Nicobar Islands.
• They are characterized by heavy leaching due to high rainfall which leads to the leaching away of siliceous material and lime of the rocks and leaves behind oxides of iron and aluminum.
• Such soils are suitable for cultivating plantations of cashew, tea, coffee, rubber, and coconut.

The correct answer is Karnam Malleswari.

Key Points

• Karnam Malleswari is the first Indian woman to win an Olympic medal.
• She accomplished this feat during the 2000 Sydney Olympics, where she won a bronze medal in the women's 69 kg weightlifting category.
• This landmark achievement marked a significant milestone in the history of Indian women participating in international sports events.
• Karnam Malleswari's success sent a strong message to Indian women, encouraging them to pursue sports actively and professionally.
• Her win paved the way for more Indian women athletes to aim for success in the Olympic Games and has been a source of inspiration to many Indian sportswomen who succeeded her.

Additional Information

• Mirabai Chanu:
• Mirabai Chanu is an accomplished Indian weightlifter.
• At the 2020 Tokyo Olympics, she won a silver medal in the Women's 49 kg category.
• This was India's first medal in the event and also made her the second Indian woman weightlifter to win an Olympic medal after Karnam Malleswari.
• PV Sindhu:
• PV Sindhu is a professional badminton player from India.
• She made history when she became the first Indian woman to win a silver medal in the 2016 Rio Olympics in the singles badminton event.
• She also clinched a bronze medal in the Tokyo 2020 Olympics making her the first Indian woman to win two Olympic medals.
• Saina Nehwal:
• Saina Nehwal is an Indian professional badminton singles player.
• She was the first Indian badminton player to win an Olympic medal, a bronze, in the 2012 London Olympics.
• Nehwal has several other accomplishments, including being the first Indian to win the BWF World Championships and the first Indian woman to reach the World No.1 ranking.

The correct answer is 2 and 3 only.

Key Points

• According to Article 318 of the Indian Constitution, the President of India and not the Parliament has the power to determine the conditions of service of the Chairman and other members of the UPSC. Hence, Statement A is incorrect.
• The Government of India Act, of 1935, envisaged a Public Service Commission for the Federation and a Provincial Public Service Commission for each Province or group of Provinces. Hence, Statement B is correct. Under the Government of India Act 1935, provision was made for a Federal Public Service Commission. Its constitution and regulations were considerably identical to the current UPSC.
• The Federal Public Service Commission came to be known as the Union Public Service Commission by virtue of Clause (1) of Article 378 of the Constitution in 1950. Hence, Statement C is also correct. The Federal Public Service Commission, established under the Government of India Act, 1935, was replaced by the Union Public Service Commission after the Constitution of India came into effect in 1950. The constitutional provision cited (Article 378 (1)) mentions this transition.

The correct answer is Article 18.

Key Points

• Article 18 of the Indian Constitution discusses the 'abolition of titles'.
• Within this article, it is expressed that the State cannot confer any titles, and citizens of India cannot accept titles from a foreign State.
• This Article is integral to the principle of equality that the Constitution of India strongly advocates.
• It is meant to preserve and promote the notion of equal recognition and respect for all citizens, irrespective of their socioeconomic status.
• However, this does not apply to academic or military distinctions. So, educational and military awards are allowed to be employed and do not come under the purview of Article 18.

Additional Information

• Article 20:
• Article 20 of the Indian Constitution provides safeguards to individuals with respect to conviction for offences.
• It grants three main rights: protection from ex post facto laws, prohibition of double jeopardy, and protection against self-incrimination.
• These rights are considered fundamental as they safeguard individual liberties from arbitrary encroachment by the state.
• Article 19:
• Article 19 gives all citizens the right to freedom of speech and expression, assembly, association, movement, residence, and profession.
• It is instrumental in maintaining the democratic fabric of the nation, as it ensures the fundamental freedoms necessary for individuals to question, articulate and participate in the governing process.
• However, these freedoms come with reasonable restrictions mentioned in the constitution itself to maintain public order, decency or morality, and national security.
• Article 17:
• Article 17 of the Indian Constitution abolishes "untouchability", and its practice in any form is forbidden.
• This provision comes under the Right to Equality, embodying the fight against social discrimination.
• It was an essential step towards an inclusive society and eliminating caste-based discrimination. Violation of this Article is punishable in accordance with the law.

The correct answer is When water vapour is present in the air.

Key Points

• Humidity refers to the presence of water vapour in the air.
• It is an essential measurement in meteorology and is vital to weather forecasts and climatic conditions.
• The level of humidity has implications for human comfort and health.
• High humidity can make temperatures feel warmer than they are, while low humidity can result in dry skin and other discomforts.
• There are different methods to measure humidity such as absolute humidity, relative humidity, and specific humidity.
• Relative humidity, which is the ratio of the amount of water vapour in the air at a certain temperature to the maximum amount that the air can hold at that temperature, is the most commonly used.
• Understanding humidity is crucial in various fields, such as aviation, construction, HVAC systems design, painting & coating, and even in understanding the spread and intensity of certain infectious diseases.

The correct answer is Canada.

Key Points

• The Komagata Maru was a Japanese steamship carrying passengers from British India in 1914.
• The intended destination of these passengers was Canada.
• Upon reaching Canadian waters, the ship was denied permission to dock.
• Most of the passengers were forced to return to India.
• This incident highlighted the discriminatory immigration policies of Canada based on the assumption that Canada was a "white man's country".
• The event also led to criticism of the unfairness of British rule in India.
• Canadian authorities refused to allow the passengers to disembark when the ship arrived at Vancouver's Burrard Inlet in late May 1914.

The correct answer is Navratri.

Key Points

• Navratri typically involves the worship of the goddess Durga, commemorated in nine different forms over the course of the festival.
• Garba is a popular folk dance native to Gujarat, a state in western India.
• Its performance is central to Navratri celebrations in Gujarat and is now popular all over India and among Indian communities worldwide.
• Beyond Navratri, Garba is also performed during other special occasions in Gujarat, indicating its cultural importance.
• The tradition of Garba, along with another dance form called Raas, is also being promoted to wider audiences, demonstrating the cultural heritage of Gujarat and fostering community ties.

Additional Information

• Pongal:
• Pongal is a major harvest festival celebrated in Tamil Nadu, a southern state in India. It typically falls in mid-January.
• The festival is named after the Tamil word "pongal," which means "to boil over," symbolizing prosperity and abundance.
• It is traditionally marked by cooking a special dish called 'Pongal' - made from newly-harvested rice boiled in milk with jaggery.
• Diwali:
• Diwali, also known as Deepavali, is a major Hindu festival celebrated by millions worldwide.
• Known as the "festival of lights," it symbolizes the triumph of light over darkness and good over evil.
• The festival involves lighting lamps and fireworks, decorating homes, feasting on sweets, and exchanging gifts.
• Bihu:
• Bihu is a set of three important cultural festivals celebrated in Assam, a northeastern state in India.
• These festivals, celebrated throughout the year, mark the changing seasons and are significant for agriculture.
• The most recognized Bihu, Rongali Bihu, celebrates the onset of the Assamese New Year and the spring season.
• Bihu dance and music are integral parts of the celebrations, and these have become emblematic of Assamese culture.

The correct answer is Maharashtra and Madhya Pradesh.

Key Points

• In December 2021, the Supreme Court of India suspended the OBC (Other Backward Classes) quota in local body elections.
• The states affected were Maharashtra and Madhya Pradesh.
• This ruling translates to the fact that state election commissions can no longer reserve seats for OBCs in all future local body elections across India.
• The condition to reinstate quotas is to comply with the Supreme Court's triple-test guidelines which include establishing the backwardness of class, inadequacy of representation and overall efficiency.
• This decision has caused significant debate regarding reservation policies in local governance and their overall impact on social justice and representation.

The correct answer is Hornbill festival.

Key Points

• The Hornbill festival was started by the Government of Nagaland in 2000.
• The objective of the festival is to encourage interaction among the various tribes of Nagaland.
• It also aims to promote and preserve the cultural heritage and traditions of the state.
• It is sometimes referred to as the "festival of festivals" because it represents all the ethnic tribes in Nagaland.
• The Hornbill Festival is celebrated from 1^st to 10^th December every year and has been highly successful.

Additional Information

• Nazu festival:
• The Nazu festival is a major celebration among the Pochury tribe of Nagaland.
• This pre-sowing festival takes place for 10 days before the sowing season begins, typically in February.
• It is marked by merrymaking, songs, dances, and games.
• Gaan-Ngai festival:
• Gaan-Ngai is the biggest festival of the Zeliangrong community.
• The Zeliangrong community is a conglomeration of three tribes: Zeme, Liangmai, and Rongmei, found in North-Eastern states of India, primarily Nagaland, Manipur, and Assam.
• This post-harvest festival happens in December/January and stretches for five days.
• It involves various traditional rituals and colourful cultural performances.
• Nuakhai festival:
• Nuakhai is an agricultural festival celebrated primarily in the Western part of Odisha to mark the arrival of the new rice harvest.
• It's a significant social/communal gathering where the goddesses are invoked before the first grain of new crop.
• The new harvest is celebrated with dances, songs, and a variety of local cuisines.

The correct answer is 17.

Key Points

• The Industrial Policy Resolution of 1956 in India classified industries into three categories: Schedule A, B, and C.
• There were 17 industries listed under Schedule A.
• The industries under Schedule A were the ones where the state would have exclusive responsibility.
• The purpose of such categorization was to help in the systematic development of various sectors in India.
• Some of the sectors under Schedule A included arms and ammunition, atomic energy, iron and steel, heavy machinery, mineral oil, coal, etc.
• The Initiative was a part of India's broader 'socialistic pattern of society' approach where the state played a dominant role in industrial development.

Additional Information

• Schedule B:
• Schedule B consisted of 12 industries.
• These industries were to be progressively state-owned, but private enterprise could also supplement the effort.
• This schedule included industries such as aluminium and other non-ferrous metals, machine tools, electrical engineering, automobiles and tractors, industrial and agricultural chemicals, and more.
• Schedule C:
• Schedule C covered the rest of the industries, and they were left open to the private sector, although the state could also venture.
• This implied that the rest of the industries not specified in Schedule A or B could be initiated and operated by private enterprises.
• The government could also start any new industry in this category, depending on the national interest.

This policy intended to maintain a balance between public and private sectors, providing ample opportunities for private entities while the State assumed responsibility for industrial development in certain sectors.

The correct answer is a-b-c-d.

Key Points

• According to the latest HDI report, Sri Lanka has the highest rank among the four countries, with an HDI value of 0.782 and a rank of 73 out of 191 countries. It falls under the high human development category.
• Maldives has the second highest rank among the four countries, with an HDI value of 0.743 and a rank of 90 out of 191 countries. It also falls under the high human development category.
• Bhutan has the third highest rank among the four countries, with an HDI value of 0.654 and a rank of 127 out of 191 countries. It falls under the medium human development category.
• Bangladesh has the lowest rank among the four countries, with an HDI value of 0.647 and a rank of 129 out of 191 countries. It also falls under the medium human development category.

Additional Information

• Human Development Index (HDI): 
• India ranked 132 out of 191 countries in the 2021 human development index.
• The report was released by the United Nations Development Program(UNDP).
• The Human Development Index was created to emphasize that people's social and economic factors should be the ultimate criteria for assessing the development of a country, not economic growth alone.
• UNDP was established in the year 1965.
• The main goal of UNDP is to help proper nations develop Their Human and Natural resources more fully.
• The UNDP projects provide support to every economic and social sector of the Agriculture Industry, Education and Science, Health and Social welfare, etc.
• Its headquarters is located in New  York.

The correct answer is Eastern Railway.

Key Points

• Asansol, Howrah, Malda, and Sealdah divisions come under the Eastern Railway zone of India.
• The Eastern Railway is one of the 19 railway zones in India.
• It is headquartered at Fairley Place, Kolkata.
• These divisions, like others in the Indian Railways, each have a Divisional Railway Manager (DRM) who reports to the General Manager of the zone.
• These divisions primarily manage the operations and maintenance of the railways under their jurisdiction.
• Eastern Railway is one of the earliest zones established by the Indian Railways and is important for passenger and freight transportation.

Additional Information

• Indian Railways is one of the largest rail networks in the world. It spans over 68,000 km, connecting almost every major city and town in India.
• As of 2025, the Indian Railways is organized into 19 zones, which are further divided into a total of 70 divisions. Each zone is headed by a General Manager, and the divisions are managed by Divisional Railway Managers.
• These zones were mostly reorganized based on linguistic and operational feasibility.
• Some of the major zones include the Northern Railway (headquartered in Delhi), Western Railway (headquartered in Mumbai), Eastern Railway (headquartered in Kolkata), and Southern Railway (headquartered in Chennai).
• The Indian Railways plays a key role in India's economy and is a significant employer. It has over 1.4 million employees and contributes to both passenger transport and freight operations in the country.
• Indian Railways has been integrating technology into its operations to improve efficiency and user experience. This includes computerized ticket booking, live tracking of trains, digital payments, and an online complaint management system.

The correct answer is Flame cells.

Key Points

• Flame cells are specialized cells that form part of the excretory system in these organisms, known as protonephridia.
• Flame cells play a primary role in osmoregulation, the process by which a balance of water and ions is maintained within the body.
• Along with osmoregulation, flame cells also help in the removal of waste products.
• This system is not only found in Platyhelminthes but also in other types of flatworms and invertebrates. However, it is most prominent in Platyhelminthes.

Additional Information

• Nerve cells:
• Platyhelminthes have a decentralized nerve cell network and two longitudinal nerve cords running along their body length.
• These nerve cells, also known as neurons, are responsible for transmitting signals across the organism.
• They enable sensing the environment and coordinating the organism's response to it.
• Ganglia:
• Ganglia are simple forms of "brains" or collections of nerve cell bodies that process information in invertebrates such as Platyhelminthes.
• They serve as the central nervous system in these organisms, acting as control centres that coordinate nerve signals.
• Hooks:
• Some Platyhelminthes, specifically parasitic ones, have hooks and suckers.
• These structures are not cells, but adaptations that help the worm to attach to the host's tissue.
• The hooks assist in anchoring the parasite to its host and facilitate the feeding process.

The correct answer is Captain Abhilasha Barak.

Key Points

• Captain Abhilasha Barak is the first woman officer to join the Army Aviation Corps as a Combat Aviator.
• She achieved this milestone after successfully completing her training in May 2022.
• Her accomplishment represents a significant step in the increasing participation of women in the Indian armed forces.
• This achievement highlights the progress in creating more equal opportunities for women in sectors historically dominated by men, such as the military.
• It also demonstrates the readiness and capability of women to take on challenging roles in areas like combat aviation.
• This accomplishment will certainly inspire more women to consider careers in the military and other related fields.

The correct answer is Ahmednagar.

Key Points

• Malik Ambar was an able administrator of the Ahmadnagar Sultanate.
• He hailed from the Deccan region of India.
• Malik Ambar played a significant role in resisting the Mughal incursions into the Deccan region during his tenure.
• Notably, despite being sold as a slave and brought to India in his youth, he rose to substantial power and influence.
• He is known for his military and administrative skills, which were instrumental in his successful resistance against the Mughals.
• His strategic prowess earned him significant recognition and his leadership was a key factor in keeping the Ahmednagar Sultanate independent for as long as it was.

The correct answer is Annapurna Devi.

Key Points

• Annapurna Devi is associated with the musical instrument Surbahar.
• Annapurna Devi was an Indian surbahar player of Hindustani classical music.
• She was also a renowned music teacher in the Maihar gharana, a school of Hindustani classical music.
• She was one of the most respected and eminent musicians of the 20^th century in India.
• The Surbahar is a stringed instrument often described as the bass sitar, and it is primarily used in Hindustani classical music.
• Annapurna Devi's mastery of the Surbahar contributed significantly to the popularity and recognition of the instrument.

Additional Information

• Shiv Kumar Sharma:
• Shiv Kumar Sharma is an iconic Indian music composer and santoor player, and he is largely responsible for making the santoor a popular Classical instrument.
• He was born in Jammu and brought the tradition of playing the santoor, hitherto a folk instrument of Jammu and Kashmir, to the Indian classical music mainstream.
• Sharma has composed music for many Hindi films in collaboration with Hariprasad Chaurasia, forming a group called Shiv-Hari.
• Sharan Rani:
• Sharan Rani was an Indian classical Sarod player and she is often referred to as the 'Sarod Rani'.
• Rani made a significant contribution to popularising Indian classical music and was one of the few famous women instrumentalists in the mid-20^th century.
• She was also the first internationally acclaimed woman performer on the Sarod.

The correct answer is Padma Shri.

Key Points

• Matha B Manjamma was conferred the Padma Shri award in 2021 by President Ram Nath Kovind.
• She was awarded in recognition of her contribution to Jogati Nritya and other folk forms.
• Matha B Manjamma Jogati is a renowned transgender folk dancer hailing from Karnataka, India.
• Matha Jogati has been preserving and promoting the traditional folk art forms of Karnataka for many years and her focus has been on Jogati Nritya, a traditional dance form performed by the Jogappa community to which she belongs.
• Along with her artistic contribution, she has worked actively for the welfare of her marginalized community.
• The Padma Shri is the fourth highest civilian award in the Republic of India, after the Bharat Ratna, the Padma Vibhushan and the Padma Bhushan.

Additional Information

• Padma Bhushan:
• The Padma Bhushan is the third-highest civilian award in the Republic of India, following the Bharat Ratna and the Padma Vibhushan, and preceding the Padma Shri.
• Instituted on 2^nd January 1954, the award is given for "distinguished service of a high order" without distinction of race, occupation, position, or sex.
• The recipients receive a Sanad (certificate) signed by the President of India and a medallion.
• Padma Vibhushan:
• The Padma Vibhushan is the second-highest civilian award in India, after the Bharat Ratna.
• It recognizes exceptional and distinguished service to the nation in any field, including government service.
• The award was established in 1954 and includes a certificate and a medallion.
• Sangeet Natak Akademi:
• The Sangeet Natak Akademi is the national-level academy for performing arts set up by the Government of India.
• It bestows awards to practising artists in the field of dance, music, and drama and also for contribution/scholarship in performing arts.
• It aims to promote the incredible wealth of the performing arts in India and preserve the diverse artistic traditions of the country.

The correct answer is Dutee Chand.

Key Points

• Dutee Chand was awarded the Chhattisgarh Veerni Award in 2021.
• Dutee Chand is an Indian professional sprinter and a national champion in women's 100 metres event.
• The award recognizes the contribution of Indian women in different fields, including sports.
• This award is an initiative by the Chhattisgarh state government to honour the outstanding work of women in various sectors.
• The award aims to uplift and motivate women in India to reach greater heights and make significant contributions to society and their respective fields.
• Dutee Chand receiving this award emphasizes her contribution to Indian sports, notably through her sprinting records and her efforts to promote athletics in India.

Additional Information

• Shikhar Dhawan:
• Shikhar Dhawan is a renowned cricketer in the Indian national team, known for his role as an opening batsman.
• His cricketing talent came to light when he scored the fastest century on Test debut against Australia in 2013.
• He played a significant role in India bagging the Champions Trophy in 2013.
• Bajrang Punia:
• Bajrang Punia is an Indian freestyle wrestler.
• He has represented India at the Olympics and other international competitions, earning numerous accolades.
• Punia became the first Indian wrestler to win two World Championships medals.
• P V Sindhu:
• P V Sindhu, or Pusarla Venkata Sindhu, is an Indian professional badminton player.
• She received global recognition when she became the first Indian to win the BWF World Championships in 2019.
• Sindhu has been a silver medalist in the Olympics and is one of the leading badminton players in the nation.

The correct answer is Pteridophyta.

Key Points

• Ferns, horsetails, and lycophytes all belong to the group referred to as Pteridophyta.
• These represent some of the earlier forms of vascular plants on Earth.
• They are classified as a subdivision of the plant kingdom, known as cryptogams, which do not produce seeds or flowers.
• Pteridophyta plants reproduce via spores, which are usually located on the underside of the fronds (leaves) in organs or structures called sporangia.
• The life cycle of Pteridophytes includes two distinct phases – the large, prominent sporophyte and a less visible, but still independent gametophyte also known as a prothallium.
• These plants are typically found in damp, shaded areas, though some have adapted to a variety of other habitats. Ferns, in particular, are known for their feather-like fronds and intricate patterns.

Additional Information

• Bryophyta:
• Bryophyta constitute the group of plants known as mosses and liverworts.
• They often grow in moist, shaded areas and are non-vascular, meaning they lack tissues for transporting water and nutrients.
• Unlike ferns, mosses reproduce using spores but are more primitive, often growing low to the ground.
• Algae:
• Algae is a diverse group of aquatic, photosynthetic organisms.
• They form a crucial part of the food chain in aquatic ecosystems and can range from microscopic sizes (microalgae) to massive kelp.
• Algae is not a homogeneous group but a term used to describe organisms from different evolutionary backgrounds that share some common features.
• Fungi:
• Fungi are a kingdom of usually multicellular eukaryotic organisms which are heterotrophic, meaning they obtain nutrients by consuming organic matter.
• They play a crucial role in nutrient cycling in ecosystems and include yeasts, molds, and mushrooms.
• Some fungi form symbiotic relationships with plants, aiding in nutrient absorption, while others can be pathogenic, causing diseases in plants and animals.

The correct answer is Sanskrit Grammar.

Key Points

• Ashtadhyayi, also known as Astadhyayi, is a renowned work on Sanskrit Grammar.
• This treatise was written by the ancient Indian grammarian Panini between the 6^th and 5^th century BC.
• It set the linguistic standards for Classical Sanskrit and is deemed to be the earliest systematic grammar of Sanskrit.
• Ashtadhyayi is composed of approximately 4,000 sutras and is organized into eight chapters, hence the name "Ashtadhyayi," which translates to "Eight Chapters."
• This work not only covers grammar but also incorporates the science of phonetics, particularly as it was understood within the ancient **Vedic tradition.**​

Additional Information

The correct answer is At room temperature, surface tension of water is less than ethyl alcohol. 

Key Points

• Surface tension is indeed typically measured in dynes/cm, which indicates the force required to break a film of length 1 cm. Hence, option 1 is correct.
• The shape of a water droplet is spherical due to surface tension. Hence, option 2 is also correct.
• The spherical shape is the result of surface tension minimizing the surface area of the drop, as the sphere is the shape that has the least surface area for a given volume.
• Contrary to statement 3, at room temperature, the surface tension of water is actually higher than that of ethyl alcohol. For example, water at 20°C has a surface tension of 72.8 dynes/cm, while that for ethyl alcohol is 22.3 dynes/cm.
• The cohesive forces between liquid molecules are indeed responsible for the phenomenon known as surface tension. These forces cause the liquid to behave as though it is covered with a stretched elastic sheet, a property known as surface tension. Hence, option 4 is also correct.

The correct answer is saving deposits with post office.

Key Points

• M₂ includes all components of M₁ (which comprises currency in the hands of the public and demand deposits, or other liquid deposits), plus savings deposits (including money market deposit accounts), small-denomination time deposits (certificates of deposit, or CDs, of under $100,000), and retail (small-denomination) money market mutual fund shares.
• These elements are seen as "near money" and can be readily converted to cash, therefore, they are included in the broader measure of the money supply known as M₂.
• Post office savings are included as they are a type of savings deposit. National Saving Certificates, coins and currency notes, and demand deposits are not added to M₁ to get M₂, as these are either already accounted for in M₁ or are different form of savings assets.
• Please note that exact components of M₂ may vary slightly between different countries depending on their banking and financial systems$.

The correct answer is 1878.

Key Points

• The Vernacular Press Act was enacted in British India in the year 1878.
• This law was enforced by the British to curtail the freedom of the Indian-language press.
• The Act was used to prevent the expression of criticism toward British policies, notably, the opposition that had grown with the outset of the Second Anglo-Afghan War (1878-80)
• It was enacted when Lord Lytton was Viceroy of India; he was known for his controversial and suppressive policies during his tenure.
• The act stated that any press printing in Vernacular language had to declare all its printing machinery and submit all material for scrutiny before publication. If the content was inflammable or criticised British authorities, it would result in the confiscation of the press.
• It was the first legislation to curtail press freedom in India, and the press became a medium of both control and revolt during British rule.
• The act provoked widespread criticism and protest by Indians. It eventually became one of the contributing factors to the nationalistic movements that emerged at the end of the 19^th century.
• The Act was, however**, repealed in 1882 by Lytton's successor, Lord Ripon,** in a move to foster press freedom in India.

The correct answer is d.

Key Points

• Each of the three oxygen atoms in an O₃ molecule has six valence electrons. This totals 18 valence electrons for the molecule.
• In the central oxygen atom, two bonds are formed: one with each of the two other Oxygen atoms.
• It utilizes 4 out of 18 electrons, leaving us with 14 electrons.
• The rest of the 14 electrons are distributed as lone pairs. Each oxygen atom receives three lone pairs (2 electrons form a pair), which account for 6 x 3 = 18 electrons. This includes the electrons shared in the bonds.
• But for total 18 electrons, two electrons are needed from somewhere else.
• These electron pair is provided by another oxygen atom, forming a double bond between the central oxygen and one of the peripheral oxygen atoms.

So, the Lewis structure of O3 can be denoted as O-O=O, where "-" denotes a single bond containing 2 electrons and "=" denotes a double bond which contains 4 electrons. One oxygen forms a single bond with the central oxygen, while another forms a double bond. Each oxygen atom also has 6 electrons (or 3 pairs) forming lone pairs around them.

Given:

(1^st natural number - 2^nd natural number)3 = 1728

1^st natural number × 2^nd natural number = 108

Formula used:

(A + B)3 = A3 + B3 + 3AB × (A + B)

Calculation:

Let 1^st natural number = A

2^nd natural number = B

(A - B)3 = 1728

⇒ (A - B) = 3√1728 = 12

squaring both sides

⇒ (A - B)² = 144

⇒ A² + B² - 2AB = 144

⇒ A2 + B2 = 144 + 216 = 360

Now,

(A + B) = √(A2 + B2 + 2AB)

⇒ √(360 + 216) = √576 = 24

(A + B)3 = A3 + B3 + 3AB × (A + B)

⇒ A3 + B3 = (A + B)3 - 3AB × (A + B)

⇒ (24)³ - 3 × 108 × 24

⇒ 13824 - 7776

⇒ 6048 

∴ The correct answer is 6048.

Shortcut Trick

Remaining work in terms of man-days = 30 men × (12 − 6) days = 180 man-days.

New total men = 30 + 24 = 54 men.

Remaining days = 180 ÷ 54 = 10 ÷ 3 = 3(1/3) days.

∴ The correct answer is 3(1/3) days.

Alternate Method

Given: Initial men = 30, Total days = 12, Joined men = 24 after 6 days.

Formula: Total Work = Men × Days

⇒ Total Work = 30 × 12 = 360 units

⇒ Work done in 6 days = 30 × 6 = 180 units

⇒ Remaining Work = 360 − 180 = 180 units

⇒ New Strength = 30 + 24 = 54 men

⇒ Days required = Remaining Work ÷ New Strength

⇒ Days = 180 ÷ 54 = 30 ÷ 9 = 10 ÷ 3 = 3(1/3) days

∴ The correct answer is 3(1/3) days.

Additional Information

Chain Rule Formula

The relationship between men, days, and work is given by (M₁×D₁)/W₁ = (M₂×D₂)/W₂.

Man-Day Concept

Total work is the product of the number of persons and the time taken, expressed in units like man-hours or man-days.

Inverse Proportion

For a constant amount of work, the number of men is inversely proportional to the number of days taken.

Shortcut Trick

Ratio of Speed (Policeman : Thief) = 40 : 32 = 5 : 4

Since Time is constant, the ratio of Distance = Ratio of Speed = 5 : 4

Difference in distance ratio = 5 − 4 = 1 unit

Given, 1 unit (initial gap) = 400 m

Distance run by the Thief = 4 units = 4 × 400 m = 1600 m

∴ The correct answer is 1600 m.

Alternate Method

Given:

Distance between Policeman and Thief = 400 m

Speed of Thief (S_T) = 32 km/h

Speed of Policeman (S_P) = 40 km/h

Formula: Relative Speed = S₁ − S₂ (when moving in the same direction)

Calculations:

⇒ Relative Speed = 40 − 32 = 8 km/h

⇒ Relative Speed in m/s = 8 × (5/18) = 20/9 m/s

⇒ Time taken to catch the thief = Distance ÷ Relative Speed

⇒ Time taken = 400 ÷ (20/9) = (400 × 9) ÷ 20 = 180 seconds

⇒ Distance run by the Thief = Speed of thief × Time

⇒ Speed of Thief in m/s = 32 × (5/18) = 80/9 m/s

⇒ Distance = (80/9) × 180 = 80 × 20 = 1600 m

∴ The correct answer is 1600 m.

Additional Information

Relative Speed in Same Direction

When two objects move in the same direction with speeds u and v, their relative speed is (u − v).

Constant Time Property

If two objects start and stop at the same time, the distance traveled by each is directly proportional to their speed (D₁/D₂ = S₁/S₂).

Unit Conversion

To convert speed from km/h to m/s, multiply by (5/18). To convert from m/s to km/h, multiply by (18/5).

Given:

(1^st natural number - 2^nd natural number)³ = 1728

1^st natural number × 2^nd natural number = 108

Formula used:

(A - B)³ = A³ - B³ - 3AB × (A - B)

Calculation:

Let 1^st natural number = A

2^nd natural number = B

(A - B)³ = 1728

⇒ (A - B) = ³√1728 = 12

A³ - B³ = (A - B)³ + 3AB × (A - B)

⇒ 1728 + 3 × 108 × 12

⇒ 1728 + 3 × 108 × 12

⇒ 1728 + 3888 = 5616

∴ The correct answer is 5616.

Calculation:

Number of male students who opted biology in school A = (900 × 30% × 7)/15 = 126

Number of male students who opted biology in school D = (800 × 18% × 5)/12 = 60

Number of female students who opted biology in school A = (900 × 30% × 8)/15 = 144

Number of female students who opted biology in school D = (800 × 18% × 7)/12 = 84

Male students who opted for biology in schools A and D : Female students who opted for biology in schools A and D

⇒ (126 + 60) : (144 + 84)

⇒ 186 : 228 = 31 : 38

∴ The correct answer is 31 : 38.

Given:

Height of tent (H) = 10 m

Base diameter (D) = 48 m

Formula used:

The curved surface area of the cone = π × R × l

Where, l = √(H² + R²) 

R = radius ; l = slant height

Calculation:

Base diameter (D) = 48 m

Base radius (R) = 48/2 = 24 m

Slant height (l) = √(H2 + R2)

⇒ √{(10)2 + (24)2}

⇒ √{100 + 576} = √676

⇒ 26 m

The curved surface area of the cone = π × R × l

⇒ π × 24 × 26 = 624 π m² 

∴ The correct answer is 624 π m2.

Calculation:

The sale of sports bicycles in 2020 = 200

The sale of sports bicycles in 2021 = 145

Percent decrement in sales of sports bicycles = {(200 - 145) × 100}/200

⇒ 55/2 = 27.5%

∴ The correct answer is 27.5%.

Formula used:

Sin (A - B) = sin A × cos B - cos A × sin B

Sin (A + B) = sin A × cos B + cos A × sin B

Calculation:

$\rm \left(\frac{\sin (x-y)}{\sin(x+y)}\right)\rm \left(\frac{\tan x+\tan y}{\tan x-\tan y}\right)$

⇒ (sin x × cos y - cos x × sin y)/(sin x × cos y + cos x × sin y) × {(sin x/cos x) + (sin y/cos y)}/{(sin x/cos x) + (sin y/cos y)}

⇒ (sin x × cos y - cos x × sin y)/(sin x × cos y + cos x × sin y) × {(sin x × cos y) + (sin y × cos x/(cos x) × (cos y)}/{(sinx × cos y) + (sin y × cos x)/(cos x) × (cosy)}

⇒ (sin x × cos y - cos x × sin y)/(sin x × cos y + cos x × sin y) × (sin x × cos y) + (siny × cos x)/(sin x × cos y) + (sin y × cos x)

⇒ 1

∴ The correct answer is 1.

Alternate MethodCalculation:

if we put x = 45° and y = 0° then,

$\rm \left(\frac{\sin (x-y)}{\sin(x+y)}\right)\rm \left(\frac{\tan x+\tan y}{\tan x-\tan y}\right)$ 

⇒ sin (45 - 0)/sin(45 + 0) × {(tan 45 + tan 0)/(tan 45 - tan 0)}

⇒ sin 45/sin 45 × {(1 + 0)/(1 - 0)} 

⇒ 1

∴ The correct answer is 1.

Shortcut Trick

Let a = 326 and b = 222.

The given expression is in the form of: ((a + b)² − (a − b)²) ÷ (a × b)

Using the standard algebraic identity: (a + b)² − (a − b)² = 4ab

Substituting this in the expression gives: 4ab ÷ ab = 4.

∴ The correct answer is 4.

Alternate Method

Given Expression:

((326 + 222)² − (326 − 222)²) ÷ (326 × 222)

Formula Used:

By using the standard expansions:

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab + b²

Subtracting the second equation from the first:

(a + b)² − (a − b)² = 4ab

Calculations:

Let a = 326 and b = 222.

⇒ Numerator = (326 + 222)² − (326 − 222)²

⇒ Numerator = 4 × 326 × 222

⇒ Denominator = 326 × 222

⇒ Expression = (4 × 326 × 222) ÷ (326 × 222)

⇒ Expression = 4

∴ The correct answer is 4.

Additional Information

Algebraic Identity for Sum of Squares

The sum of the squares of the sum and difference of two numbers is given by: (a + b)² + (a − b)² = 2(a² + b²).

Difference of Squares Identity

The difference of the squares of two numbers is factorized as: a² − b² = (a − b)(a + b).

Square of a Trinomial

The square of the sum of three terms is given by: (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca.

Given:

First number (a) = (x2 - y2)

Second number (b) = (x - y)

Formula used:

Third proportional = {2^nd number (b)}²/first number (a)

(x2 - y2) = (x - y) × (x + y)

Calculation:

Third proportional = (x - y)²/(x2 - y2)

⇒ {(x - y) × (x - y)}/{(x - y) × (x + y)} 

⇒ $\rm \frac{x-y}{x+y}$

∴ The correct answer is $\rm \frac{x-y}{x+y}$.

Formula used:

Effective discount = D₁% + D₂% - (D1 × D2)/100

Discount = (free product × 100)/Total product

Calculation:

For case A :

Effective discount = D1% + D2% - (D1 × D2)/100

⇒ 10 + 15 - (10 × 15)/100 = 25 - 1.5

⇒ 23.5%

For case B:

Total discount = (free product × 100)/Total product

⇒ (2 × 100)/7 = 28.56%

∴ The correct option is 2.

Given:

A can finish a work = 20 days

B can complete the same work = 15 days

Formula used:

Total work = efficiency × time

Calculation:

According to the question:

⇒ B × 9 + A × D = 60

⇒ 4 × 9 + 3 × D = 60

⇒ 3D = (60 - 36) = 24

⇒ D = 24/3 = 8 days

∴ The correct answer is 8 days.

Shortcut Trick

Relative Speed (Same Direction) = 144 − 108 = 36 km/h

Convert to m/s: 36 × (5/18) = 10 m/s

Total Distance = Sum of lengths = 320 + 540 = 860 m

Time Taken = Total Distance ÷ Relative Speed = 860 ÷ 10 = 86 s

∴ The correct answer is 86 s.

Alternate Method

Given: Length of Train P = 320 m, Length of Train Q = 540 m, Speed of P = 108 km/h, Speed of Q = 144 km/h

Formula Used: Time = Total Distance ÷ Relative Speed

⇒ Total Distance = 320 + 540 = 860 m

⇒ Relative Speed = 144 − 108 = 36 km/h

⇒ Speed in m/s = 36 × (5/18) = 10 m/s

⇒ Time = 860 ÷ 10

⇒ Time = 86 s

∴ The correct answer is 86 s.

Additional Information

Relative Speed Concepts

When moving in the same direction, relative speed = S₁ − S₂. When moving in the opposite direction, relative speed = S₁ + S₂.

Unit Conversion

To convert km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5.

Train Crossing a Point Object

When a train crosses a pole or a standing man, the distance covered is equal to the length of the train.

Given:

10 men can do work = 25 days

Formula used:

Total work = efficiency × time

Calculation:

Let the efficiency of a man = M

According to the question:

⇒ 10 M × 25 = 10 M × 12 + 13 M × D

⇒ 250 M - 120 M = 13 M × D

⇒ 13 M × D = 130 M

⇒ D = 130/13 = 10 days

∴ The correct answer is 10 days.

Shortcut Trick

Simple Interest is directly proportional to Time when the Principal and Rate are constant.

25% of Principal is earned in 5 years.

To make interest equal to Principal (i.e., 100% of Principal), the factor is 100 ÷ 25 = 4.

Required Time = 5 years × 4 = 20 years.

∴ The correct answer is 20 years.

Alternate Method

Given:

Simple Interest (SI) for 5 years = 25% of Principal (P)

Formula Used:

Simple Interest (SI) = (P × R × T) / 100

Where P = Principal, R = Rate of Interest, and T = Time

Calculations:

⇒ SI = 0.25P (Since SI is 25% of Principal)

⇒ 0.25P = (P × R × 5) / 100

⇒ 25 = 5 × R

⇒ R = 5% per annum

Now, we need to find Time (T) when SI = Principal (P):

⇒ P = (P × 5 × T) / 100

⇒ 1 = (5 × T) / 100

⇒ T = 100 / 5

⇒ T = 20 years

∴ The correct answer is 20 years.

Additional Information

Simple Interest Properties

Simple interest is calculated only on the initial Principal amount, making it grow linearly over time.

Amount Formula

The total Amount (A) after T years is A = P + SI = P(1 + RT/100).

Rate of Interest

The Rate (R) can be expressed as: R = (SI × 100) / (P × T).

Interest to Time Relation

If SI becomes 'n' times of the Principal, then the time taken is T = [(n × 100) / R] years.

Shortcut Trick

Factor out the lowest power: 4¹²(1 + 4¹ + 4² + 4³).

Simplify the bracket: 1 + 4 + 16 + 64 = 85.

Check divisibility of 85 by the given options: 85 ÷ 17 = 5.

Since 85 is divisible by 17, the entire expression is completely divisible by 17.

∴ The correct answer is 17.

Alternate Method

Given: The expression is 4¹² + 4¹³ + 4¹⁴ + 4¹⁵

Formula Used: a^m+n = a^m × aⁿ and taking out highest common factor.

Calculations:

⇒ 4¹² + 4¹²⁺¹ + 4¹²⁺² + 4¹²⁺³

⇒ 4¹² (4⁰ + 4¹ + 4² + 4³)

⇒ 4¹² (1 + 4 + 16 + 64)

⇒ 4¹² × 85

⇒ 4¹² × 5 × 17

⇒ As 17 is a prime factor of the resultant product, the expression is divisible by 17.

∴ The correct answer is 17.

Additional Information

Divisibility of Polynomial Sums

For expressions of the form aⁿ + aⁿ⁺¹ + ... + a^n+k, always factor out the smallest power aⁿ to analyze the numerical sum of the remaining terms.

Geometric Progression (GP) Sum

The term (1 + 4 + 4² + 4³) is a finite GP series with sum S_n = a(rⁿ − 1) ÷ (r − 1), where a = 1, r = 4, and n = 4.

Factors and Multiples

If a number N can be written as x × y, then N is divisible by all factors of x and all factors of y.

Given:

Cot A = 12/5

Formula used:

Pythagorean theorem:

H² = P² + B²

Cot A = B/P ; sin A = P/H ; cos A = B/H ; cosec A = H/P

Where, H = hypotenuse ; P = perpendicular ; B = Base

Calculation:

Cot A = 12/5 = B/P

Using Pythagorean theorem:

H2 = P2 + B2

⇒ H² = (5)² + (12)²

⇒ H = √(25 + 144) = √169

⇒ H = 13 cm

Now,

(sin A + cos A) × cosec A

⇒ {(5/13) + (12/13)} × 13/5

⇒ (17/13) × (13/5) = 17/5

∴ The correct answer is 17/5.

Shortcut Trick

Ratio of Income : Expenditure : Savings = 45000 : 33000 : 12000 = 15 : 11 : 4

Using the weighted average method: Income = Expenditure + Savings

Let the percentage increase in savings be x%.

15 × 20% = 11 × 12% + 4 × x ⇒ 300% = 132% + 4x ⇒ 4x = 168% ⇒ x = 42%

∴ The correct answer is 42%.

Alternate Method

Given:

Initial Income = ₹45,000

Initial Expenditure = ₹33,000

Income is increased by 20% and Expenditure is increased by 12%.

Formula Used:

Savings = Income − Expenditure

Percentage Increase = (Increase in Value ÷ Original Value) × 100

Calculations:

⇒ Initial Savings = ₹45,000 − ₹33,000 = ₹12,000

⇒ New Income = ₹45,000 + (20% of ₹45,000) = ₹45,000 + ₹9,000 = ₹54,000

⇒ New Expenditure = ₹33,000 + (12% of ₹33,000) = ₹33,000 + ₹3,960 = ₹36,960

⇒ New Savings = New Income − New Expenditure

⇒ New Savings = ₹54,000 − ₹36,960 = ₹17,040

⇒ Increase in Savings = ₹17,040 − ₹12,000 = ₹5,040

⇒ Percentage increase in savings = (5,040 ÷ 12,000) × 100

⇒ Percentage increase in savings = 42%

∴ The correct answer is 42%.

Additional Information

Income and Expenditure Concept

Income is always the sum of Expenditure and Savings. Any absolute or percentage change in income naturally distributes across changes in both expenditure and savings.

Weighted Average (Alligation) Method

When a base quantity is divided into two parts, the net percentage change in the total is mathematically equivalent to the weighted average of the percentage changes in its individual parts: I × I_% = E × E_% + S × S_%.

Percentage Change Formula

Percentage Change = [(Final Value − Initial Value) ÷ Initial Value] × 100. A positive result directly indicates an increase, while a negative result indicates a decrease.

Concept used:

Divisibility rule of 8:

If the last three digits of a number are divisible by 8, the number is divisible by 8.

Divisibility rule of 3:

a number is completely divisible by 3 if the sum of its digits is divisible by 3.

24 = 3 × 8

If a number is divisible by 3 and 8 then it is also divisible by 24.

Calculation:

We need to check it by option:

Option 1:

Number = 52688

Sum of digits = 5 + 2 + 6 + 8 + 8 = 29

29 is not divisible by 3. so the number is not divisible by 3.

So the number is also not divisible by 24.

Option 2:

Number = 49512

Sum of digits = 4 + 9 + 5 + 1 + 2 = 21

21 is divisible by 3. so the number is divisible by 3.

The last three digits of the number = 512

512 is divisible by 8, so the number is also divisible by 8.

So the number is divisible by 24.

∴ The correct option is 2.

Given:

The average weight of 20 people = 59.8 kg

Formula used:

Average weight = total weight of people of a group/number of people in group

Calculation:

Correct average weight = {(59.8 × 20) - 68 + 77}/20

⇒ {1196 + 9}/20

⇒ 1205/20 = 60.25 kg

∴ The correct answer is 60.25 kg.

Given:

Area of △PQR = 32 cm2

A, B, and C be the mid-points of sides PQ, QR and PR.

Concept used:

The line segment in a triangle joining the midpoint of any two sides of the triangle,

is said to be parallel to its third side and is also half of the length of the third side.

Heron's formula:

Area = √{S(S - a)(S - b)(S - c)}

Where, S = (a + b + c)/2

And a, b, and c are the sides of the triangle.

Calculation:

Semi-perimeter (S) =  (PQ + QR + PR)/2

Area of △XYZ = √S(S - p)(S - q)(S - r)

⇒ √[(PQ + QR + PR)/2 × {(PQ + QR + PR)/2 - QR} × {(PQ + QR + PR)/2 - PR} × {(PQ + QR + PR)/2 - PQ}]

⇒ √[(PQ + QR + PR)/2 × {(PQ + QR + PR) - 2QR}/2 × {(PQ + QR + PR) - 2PR}/2 × {(PQ + QR + PR) - 2PQ}/2]

⇒ √[(PQ + QR + PR)/2 × (PQ + QR + PR)/2 × (PQ + QR + PR)/2 × (PQ + QR + PR)/2]

⇒ (PQ + QR + PR)2/4 = 32 cm2 -------- (1)

With the midpoint theorem:

AC = QR/2 ; AB = PR/2 ; BC = PQ/2

Semi-perimeter (S) = (AB + BC + AC)/2

⇒ {(PR/2) + (PQ/2) + (QR/2)}/2

⇒ (PR + PQ + QR)/4

Area of △ABC = √S(S - p)(S - q)(S - r)

⇒ √[(PR + PQ + QR)/4 × {(PR + PQ + QR)/4 - QR/2} × {(PR + PQ + QR)/4 - PR/2} × {(PR + PQ + QR)/4 - PQ/2}]

⇒ √[(PR + PQ + QR)/4 × {(PR + PQ + QR) - 2QR}/4 × {(PR + PQ + QR) - 2PR}/4 × {(PR + PQ + QR) - 2PQ}/4]

⇒ √[(PR + PQ + QR)/4 × (PR + PQ + QR)/4 × (PR + PQ + QR)/4 × (PR + PQ + QR)/4]

⇒ (PR + PQ + QR)2/(4 ×4)

⇒ 32/4 = 8 cm2  ------ From (1)

∴ The correct answer is 8 cm2.

Shortcut TrickConcept used:

Area of △ABC = (1/4) × Area of △PQR

Calculation:

Area of △ABC = (1/4) × Area of △PQR

⇒ 32/4 = 8 cm2

∴ The correct answer is 8 cm2.

Given:

Radius of large circle (R) = 15 cm.

Radius of small circle (r) = 13 cm

Concept used:

A line drawn from the centre of the circle to a chord bisects the chord into two halves.

The tangent to the circle is perpendicular to the radius of the circle at the point of contact.

Pythagorean theorem:

H² = P² + B²

Where, H = hypotenuse ; P = perpendicular ; B = base

Calculation:

Here, O is the centre and PQ is the chord of the circle.

In △POR

⇒ OP² = OR² + PR²

⇒ (15)² = (13)² + PR²

⇒ PR² = 225 - 169 = 56

⇒ PR = √56 = 2√14 cm

PQ is tangent so, OR ⊥ PQ

PQ = PR + RQ

⇒ 2√14 + 2√14 (As PR = RQ)

⇒ 4√14 cm

∴ The correct answer is 4√14 cm.

Given:

Marked price (M.P) = Rs.10000

Discount (D) = Rs.500

Additional discount (D₁)% = 7%

Formula used:

If discount = D%

Selling price (S.P) = M.P × (100 - D)%

Calculation:

Selling price = (10000 - 500) = Rs.9500

Additional discount = 7%

Final S.P = 9500 × 93% = Rs.8835

∴ The correct answer is Rs.8835.

Given:

tan (A/2) = x

Formula used:

tan (A/2) = ± $\rm \frac{\sqrt{1-\cos A}}{\sqrt{1+\cos A}}$

Calculation:

tan (A/2) = x

⇒ $\rm \frac{\sqrt{1-\cos A}}{\sqrt{1+\cos A}}$ = x

⇒ x = $\rm \frac{\sqrt{1-\cos A}}{\sqrt{1+\cos A}}$

∴ The correct option is 3.

Alternate Method 

We know: tan(A/2) = sin(A/2) / cos(A/2).

 

Sin(A/2) can be derived by the Pythagorean Identity, sin²λ + cos²λ = 1, which means sinλ = √(1 - cos²λ). So, sin(A/2) = √(1 - cos²(A/2)).

 

Putting this into the equation, we get

 

tan(A/2) = √(1 - cos²(A/2)) / cos(A/2)  .......(i)

 

Now, from half angle formula, 

 

cos(A/2) = √((1 + cosA) / 2)  .......(ii)

 

value of (ii) put in equation (i):-

 

tan(A/2) = √[1 - √{(1 + cosA)²/ 4}] / √((1 + cosA) / 2)

 

tan(A/2) = √[1 - {(1 + cosA)/ 2}] / √((1 + cosA) / 2)

tan(A/2) = √((2 - 1 - cosA)/ 2) / √((1 + cosA) / 2)

tan(A/2) = √((1 - cosA)/ 2) / √((1 + cosA) / 2)

tan(A/2) = ±√(1 - cosA) / √(1 + cosA).

 

So, option 3 is the correct answer.

Given:

Radius of 1^st circle (r₁) = 10 cm

Radius of 2^nd circle (r₂) = 5 cm

Formula used:

Direct common tangent = 2 × √(r₁ × r₂)

Calculation:

 

Direct common tangent = 2 × √(r1 × r2)

⇒  2 × √(10 × 5)

⇒ 10√2 cm

∴ The correct answer is 10√2 cm.

The correct answer is: Ruined

Key Points

• Ravaged means to cause severe damage or destruction. (गंभीर क्षति या विनाश करना)
• For example: The tornado ravaged the small town, leaving behind destruction.
• Marked option Ruined means to damage something so badly that it loses all its value, pleasure, etc. (किसी चीज़ को तबाह कर देना, बरबाद कर देना)
• For example: The fire completely ruined the historic building.
• So, 'ruined' is the best synonym for "ravaged" in this context.
• The past tense form of "ruin" is "ruined", which fits perfectly in the sentence.

Therefore, the correct answer is option 3.

Additional Information

• Reaffirmed means to confirm or assert again. It does not fit the context of the sentence. (दोबारा पुष्टि या दावा करना)
• Rescinded means to revoke or cancel. It does not fit the context of the sentence. (रद्द करना)
• Retracted means to withdraw or take back. It does not fit the context of the sentence. (वापस लेना)

The correct answer is: living conditions

Key Points

• "Living conditions" is the most appropriate option as it accurately conveys the meaning of "an improvement in people's daily arrangements".
• "Living conditions" includes the provision of fundamental necessities and an increase in per capita income. This refers to the circumstances in which people live, including their housing, environment, and overall quality of life, which is directly related to daily arrangements and improvements.

Therefore, the correct answer is option 4.

Additional Information

• "diving techniques" This refers to methods used in diving and is unrelated to daily life arrangements.
• "dining categories" - This refers to types of dining or food-related classifications, which does not encompass the broader aspects of daily life.
• "existing calamities" - This refers to current disasters or misfortunes, which again does not relate to daily life improvements.

The correct answer is: Idols

Key Points

• Idols means images or representations of a god or goddess, which is the correct word to use in the given context. (किसी देवता या देवी की छवियां या प्रतिनिधित्व)
• The word is spelled with an "o" and not an "e".
• The word is a noun and can be used in the singular or plural form.
• For example: The idols of Lord Shiva and Parvati were beautifully decorated in the temple.

Therefore, the correct answer is option 1.

Complete sentence: They saw the beautiful idols of the Gods in the Temples. 

Additional Information

• 'Idoles' is misspelled with an extra "e" with it.
• Ideals means principles or standards of perfection, which does not fit the context of the sentence. (पूर्णता के सिद्धांत या मानक)
• Idles means to spend time doing nothing or being inactive, which is not relevant to the sentence. (कुछ न करने या निष्क्रिय रहने में समय व्यतीत करना)

The correct answer is: Inebriated 

Key Points

• Inebriated means intoxicated or drunk, which is the intended meaning of the sentence. (नशे में या नशे में धुत्त)
• For example: He became inebriated after drinking too much at the party.
• The word is appropriate in this context because it specifically refers to the influence of drugs and alcohol.
• It is a more formal and precise word choice than some of the other options.

Therefore, the correct answer is option 1.

Additional Information

• Simonised means to polish a motor vehicle. (मोटर वाहन को चमकाने के लिए)
• Ponied means to pay a sum of money, especially as a contribution or unavoidable expense. (धनराशि का भुगतान करना, विशेष रूप से योगदान या अपरिहार्य व्यय के रूप में)
• Pocked means marked or indented with small hollows. (छोटे-छोटे गड्ढों से चिह्नित या इंडेंट किया हुआ)

The correct answer is: Shirts are not bought by him. 

Key Points

• The sentence is in the active voice with the subject "he" performing the action of "buying shirts."
• To convert it into passive voice, we need to make the object "shirts" the subject of the sentence and add a form of "be" before the main verb "bought."
• The past participle form of "buy" is "bought," which is used in passive voice sentences.
• The sentence in passive voice becomes "Shirts are not bought by him."

Hence, option 1 is the correct answer.

Additional Information

• Option 2: The sentence changes the verb "buy" to "bring," which changes the meaning of the sentence.
• Option 3: The sentence uses the incorrect form of "been" after "were," making it grammatically incorrect.
• Option 4: The sentence is grammatically correct but conveys a negative meaning of the original sentence.